Finite Group Databasebeta

← #25133153

Subgroups — #25133153

Order 11008.

1248 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583564C211yesmaximal, characteristic
2C2×#14583192C211yesmaximal, characteristic, complemented
3C2×#14583002C211yesmaximal, characteristic
4#19139959C211yesmaximal, characteristic, complemented
5#19135922C211yesmaximal, characteristic, complemented
6#19135920C211yesmaximal, characteristic, complemented
7#19135734C211yesmaximal, characteristic, complemented
8#19135566C211yesmaximal, characteristic, complemented
9#19135533C211yesmaximal, characteristic, complemented
10#19134932C211yesmaximal, characteristic
11#19134926C211yesmaximal, characteristic
12#19134845C211yesmaximal, characteristic
13#19134843C211yesmaximal, characteristic
14#19134604C211yesmaximal, characteristic
15C43×#2024C211yesmaximal, characteristic, complemented
16C22×Q8×D43—21no—
17C22×#10621884C2211yescharacteristic
18#14583564—24no—
19#14583564—24no—
20C2×#13063324C2211yescharacteristic
21C2×#13063324C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063303—21no—
24C2×#13063301—21no—
25C2×Q8×Dic43C2211yescharacteristic
26C2×C4×Dic86C2211yescharacteristic
27C2×C4×D172C2211yescharacteristic
28C2×#13063287C2211yescharacteristic
29C2×#13063287C2211yescharacteristic
30#14583192—24no—
31#14583002—24no—
32C2×#13063259C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34C2×#13063258C2211yescharacteristic
35C2×Dic43⋊C8C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41#14582841—21no—
42#14582820—21no—
43#14582806C2211yescharacteristic
44#14582798C2211yescharacteristic
45#14582797C2211yescharacteristic
46#14582786—21no—
47#14582782—21no—
48#14582764C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4⋊Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C43×#391C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86—21no—
65C22×Dic86D411yescharacteristic
66C2×Q8×D43—28no—
67C2×Q8×D43—44no—
68C2×Q8×D43—44no—
69C22×D172C2311yescharacteristic
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C2×#10621884—22no—
74C2×#10621884—22no—
75C2×#10621884Q814yescomplemented
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063324—22no—
79#13063324—22no—
80#13063324—22no—
81#13063324D414yes—
82#13063303—28no—
83#13063303—28no—
84#13063301—28no—
85Q8×Dic43—22no—
86Q8×Dic43—22no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×D172—22no—
90C4×D172—22no—
91#13063287—22no—
92#13063287—22no—
93#13063287—22no—
94#13063287D414yes—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43D411yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4D411yescharacteristic
105C2×Dic43⋊C4D411yescharacteristic
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112#13063259—22no—
113#13063258—22no—
114#13063258—22no—
115Dic43⋊C8—22no—
116#13063249—22no—
117#13063247—22no—
118#13063247—22no—
119#13063245—22no—
120#13063235—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C22×Q8×C43—21no—
128C22×Q8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C4⋊Q8×C43—22no—
132C4⋊Q8×C43—22no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C42×C43C2311yescharacteristic
138#103×C43—22no—
139#103×C43—22no—
140#95×C43—21no—
141#95×C43—21no—
142C23×D43—21no—
143C2×Q8×C43—24no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—42no—
150C2×Q8×C43—42no—
151C2×Q8×C43C2×Q812yescomplemented
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166Q8×D43—432no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172C2×D412yes—
171C2×D172C2×Q812yes—
172C2×D172#4112yes—
173C2×C4×D43—24no—
174C2×C4×D43—24no—
175C2×C4×D43—24no—
176C2×C4×D43—42no—
177C2×C4×D43—42no—
178C2×C4×D43—42no—
179C2×C4×D43—42no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182C2×Dic86—22no—
183C2×Dic86—22no—
184C2×Dic86—22no—
185C2×Dic86—24no—
186C2×Dic86—24no—
187C2×Dic86—42no—
188C2×Dic86—42no—
189C2×Dic86—42no—
190C2×Dic86—42no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C4⋊C4×C43—24no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43C2×D412yes—
203C4⋊C4×C43C2×D412yes—
204C42×C43—21no—
205C42×C43—21no—
206#10621884—28no—
207(C2×D43)⋊C4—24no—
208(C2×D43)⋊C4—24no—
209(C2×D43)⋊C4—24no—
210C4⋊Dic43—21no—
211C4⋊Dic43—22no—
212C4⋊Dic43—21no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43—21no—
216C4⋊Dic43—42no—
217C4⋊Dic43—42no—
218C4⋊Dic43C2×D412yes—
219Dic43⋊C4—24no—
220Dic43⋊C4—24no—
221Dic43⋊C4—22no—
222Dic43⋊C4—22no—
223Dic43⋊C4—42no—
224C4×Dic43—21no—
225C4×Dic43—21no—
226C4×Dic43—42no—
227C4×Dic43C2×D412yes—
228C4×Dic43C2×D412yes—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8C2×Q812yescomplemented
235C23×C43C22×D411yescharacteristic
236C22×D43—22no—
237C22×D43—22no—
238C22×D43—22no—
239C22×D43—41no—
240C22×D43—41no—
241C22×D43—41no—
242C22×D43—41no—
243Q8×C43—22no—
244Q8×C43—22no—
245Q8×C43—48no—
246Q8×C43—41no—
247Q8×C43—41no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—22no—
252C2×C4×C43—22no—
253C2×C4×C43—22no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43AGL(1,ℤ/8)12yes—
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C22×Q811yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C432−1+411yescharacteristic
271C2×C4×C432−1+411yescharacteristic
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—22no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43#12012yes—
291C2×Dic43#12012yes—
292C2×Dic43AGL(1,ℤ/8)12yes—
293D172—22no—
294D172—22no—
295D172—22no—
296D172C22⋊Q814yes—
297C4×D43—48no—
298C4×D43—48no—
299C4×D43—48no—
300Dic86—28no—
301Dic86—48no—
302Dic86—48no—
303C8×C43—41no—
304C8×C43—41no—
305C43⋊C8—22no—
306C43⋊C8—41no—
307#24342—431nomaximal, Sylow
308C22×C43C2×#12011yescharacteristic
309C22×C43#54811yescharacteristic
310C22×C43D4×Q811yescharacteristic
311C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C43#57811yescharacteristic
314C22×C43#57811yescharacteristic
315C2×D43—24no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43—42no—
319C2×D43—42no—
320C2×D43—42no—
321C2×D43—42no—
322C4×C43—22no—
323C4×C43—42no—
324C4×C43—42no—
325C4×C43—42no—
326C4×C43—41no—
327C4×C43—81no—
328C4×C43C2×C22⋊Q811yescharacteristic
329C4×C43#53611yescharacteristic
330C4×C43#54811yescharacteristic
331C4×C43D4×Q811yescharacteristic
332Dic43—22no—
333Dic43—22no—
334Dic43—22no—
335Dic43—42no—
336Dic43—41no—
337Dic43—81no—
338Dic43—81no—
339C2×D4×Q8—431no—
340C2×#477—431no—
341C2×#440—431no—
342#2581—431no—
343#2057—431no—
344#2057—431no—
345#2024—431no—
346#2024D4311yescharacteristic, complemented
347#1993—431no—
348#1985—431no—
349#1877—431no—
350#1877—431no—
351#1862—431no—
352#1862—431no—
353#1804—431no—
354C2×C43#240911yescharacteristic
355C2×C43#300311yescharacteristic
356C2×C43#301111yescharacteristic
357C2×C43#336711yescharacteristic
358C2×C43#336711yescharacteristic
359C2×C43#338611yescharacteristic
360C2×C43#338611yescharacteristic
361D43—44no—
362C23×Q8—861no—
363C22×SD16—431no—
364D4×Q8—864no—
365D4×Q8—864no—
366C2×C4⋊Q8—431no—
367C2×C4⋊Q8—431no—
368C2×C4⋊Q8C2×D4311yescharacteristic
369C2×C22⋊Q8—861no—
370C2×C22⋊Q8—861no—
371C2×C22⋊Q8—861no—
372C2×C4×Q8—431no—
373C2×C4×Q8—431no—
374C2×C4×D4—431no—
375C2×C4×D4—431no—
376C2×C4×D4—431no—
377#477—864no—
378#440—864no—
379C2×#107—431no—
380C2×#107—431no—
381C2×#107—431no—
382C2×C4⋊C8—431no—
383C2×#103—431no—
384C2×#103C2×D4311yescharacteristic
385C2×#103C2×D4311yescharacteristic
386C2×#102—431no—
387C2×#102—431no—
388C2×#102—431no—
389C2×#97—431no—
390#400—861no—
391#395—861no—
392#391—431no—
393#391C2×D4311yescharacteristic
394#389—431no—
395#389—431no—
396#387—861no—
397#387—861no—
398#382—431no—
399#340—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340C2×D4311yescharacteristic
404#340C2×D4311yescharacteristic
405#336—431no—
406#336—431no—
407#336—431no—
408#336C2×D4311yescharacteristic
409C43#2434211yescharacteristic, complemented, Sylow
410C22×Q8—21no—
411C22×Q8—431no—
412C22×Q8—861no—
413C22×Q8—861no—
414C22×Q8—868no—
415C22×Q8—1724no—
416C22×Q8—1724no—
417C22×Q8C22×D4311yescharacteristic
418C22×D4—431no—
419C23×C4—861no—
420C23×C4—861no—
421C23×C4—861no—
422C2×SD16—434no—
423C2×SD16—862no—
424C2×SD16—862no—
425C22×C8—431no—
426C22×C8—431no—
427C22×C8C22×D4311yescharacteristic
428C22×C8C22×D4311yescharacteristic
429C4⋊Q8—22no—
430C4⋊Q8—22no—
431C4⋊Q8—434no—
432C4⋊Q8—862no—
433C4⋊Q8—862no—
434C4⋊Q8—862no—
435C22⋊Q8—868no—
436C22⋊Q8—868no—
437C22⋊Q8—868no—
438C4×Q8—862no—
439C4×Q8—862no—
440C4×Q8—862no—
441C4×Q8—862no—
442C4×D4—434no—
443C4×D4—862no—
444C4×D4—862no—
445C4×D4—862no—
446C4×D4—862no—
447C4×D4—862no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—431no—
450C2×C4⋊C4—431no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4C22×D4311yescharacteristic
461C2×C4⋊C4C22×D4311yescharacteristic
462C2×C4⋊C4C22×D4311yescharacteristic
463C2×C22⋊C4—861no—
464C2×C22⋊C4—861no—
465C2×C22⋊C4—861no—
466C2×C42—431no—
467C2×C42—431no—
468C2×C42—861no—
469C2×C42C22×D4311yescharacteristic
470#107—862no—
471#107—862no—
472#107—862no—
473C4⋊C8—862no—
474#103—22no—
475#103—22no—
476#103—862no—
477#102—862no—
478#102—862no—
479#102—862no—
480#97—862no—
481#95—21no—
482#95—21no—
483#95—861no—
484#95—861no—
485#95—861no—
486#95—861no—
487#95—861no—
488#95—861no—
489C24—861no—
490C2×Q8—24no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—862no—
499C2×Q8—862no—
500C2×Q8—864no—
501C2×Q8—864no—
502C2×Q8—862no—
503C2×Q8—1722no—
504C2×Q8—1722no—
505C2×Q8—1722no—
506C2×Q8—1722no—
507C2×Q8—17232no—
508C2×Q8Q8×D4312yescomplemented
509C2×D4—432no—
510C2×D4—432no—
511C2×D4—432no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4—861no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—431no—
522C22×C4—431no—
523C22×C4—864no—
524C22×C4—864no—
525C22×C4—864no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—1722no—
530C22×C4—1722no—
531C22×C4—1722no—
532C22×C4—1722no—
533C22×C4—1722no—
534C22×C4—1722no—
535C22×C4D4×D4311yescharacteristic
536C22×C4D4×D4311yescharacteristic
537C22×C4C23×D4311yescharacteristic
538SD16—868no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—432no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C4⋊C4—24no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—432no—
557C4⋊C4—862no—
558C4⋊C4—862no—
559C4⋊C4—862no—
560C4⋊C4—864no—
561C4⋊C4—864no—
562C4⋊C4—861no—
563C4⋊C4—861no—
564C4⋊C4—861no—
565C4⋊C4—861no—
566C4⋊C4—861no—
567C4⋊C4—1722no—
568C4⋊C4—1722no—
569C4⋊C4—1722no—
570C4⋊C4D4×D4312yes—
571C4⋊C4D4×D4312yes—
572C22⋊C4—864no—
573C22⋊C4—864no—
574C22⋊C4—864no—
575C42—21no—
576C42—21no—
577C42—432no—
578C42—432no—
579C42—861no—
580C42—861no—
581C42—1722no—
582C23—862no—
583C23—862no—
584C23—862no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23C2×D4×D4311yescharacteristic
590Q8—22no—
591Q8—22no—
592Q8—48no—
593Q8—41no—
594Q8—41no—
595Q8—868no—
596Q8—1728no—
597Q8—1728no—
598D4—434no—
599D4—862no—
600D4—862no—
601D4—862no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—432no—
620C2×C4—432no—
621C2×C4—432no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—862no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—1728no—
633C2×C4—1728no—
634C2×C4—1728no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4#1306335212yes—
644C2×C4C2×D4×D4311yescharacteristic
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4C2×Q8×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4#1306337211yescharacteristic
649C2×C4#1306337211yescharacteristic
650C8—41no—
651C8—41no—
652C8—862no—
653C8—1721no—
654C22—864no—
655C22—1722no—
656C22—1722no—
657C22—1722no—
658C22—1722no—
659C22—1722no—
660C22—1722no—
661C22#120×D4311yescharacteristic
662C22#1458355711yescharacteristic
663C22#1458356211yescharacteristic
664C22AGL(1,ℤ/8)×D4311yescharacteristic
665C22C2×#1306335211yescharacteristic
666C22#1458371211yescharacteristic
667C22#1458371511yescharacteristic
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—41no—
673C4—81no—
674C4—862no—
675C4—862no—
676C4—862no—
677C4—3441no—
678C4—3441no—
679C4—1722no—
680C4—1721no—
681C4C22⋊Q8×D4311yescharacteristic
682C4#1458346911yescharacteristic
683C4#1458355711yescharacteristic
684C4#1458356211yescharacteristic
685C2—1724no—
686C2#1913795311yescharacteristic
687C2#1914382311yescharacteristic
688C2#1914388511yescharacteristic
689C2#1914731011yescharacteristic
690C2#1914731811yescharacteristic
691C2#1914751511yescharacteristic
692C2#1914751911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2024C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2024D43
hypocenterC43#24342
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14583192C2semidirect
4. #19139959C2semidirect
5. #19135922C2semidirect
6. #19135920C2semidirect
7. #19135734C2semidirect
8. #19135566C2semidirect
9. #19135533C2semidirect
15. C43×#2024C2semidirect
75. C2×#10621884Q8semidirect
151. C2×Q8×C43C2×Q8semidirect
234. C2×C43⋊C8C2×Q8semidirect
346. #2024D43semidirect
409. C43#24342semidirect
508. C2×Q8Q8×D43semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145835642
C2×#145831922
C2×#145830022
#191399592
#191359222
#191359202
#191357342
#191355662
#191355332
#191349322
#191349262
#191348452
#191348432
#191346042
C43×#20242
#2434243